Andrius Kulikauskas

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See: Math and Math?


I very much like your idea of using spreadsheets to model different "savings and loan" arrangements.

I think that playing around with numbers is essential to building intuition. And spreadsheets seem like an excellent way to do that, especially for that kind of problem. And a very natural one that leads directly into work skills.

I think a key thing to learn is the different kinds of families of functions and their qualitative differences, such as linear vs. exponential.

If math is a study of systems, then that includes especially realizing when systems or models break down, when they apply and when they don't apply.

Among my favorite exponential modeling problems are:

  • Given the current population and current growth rate work backwards to figure out when the first person appeared ("Adam"), the second person ("Eve") and so on.
  • Native Americans in Manhattan (NY) are said to have sold the island for $24 in 1624. Supposing they invested that wisely (model different rates), what would their investment be worth today? Could they buy Manhattan back?
  • There is an old classic story about the inventors of checkers and chess in India. The king offered them to name a gift they would like to receive for each of 64 days, corresponding to the squares on the board. The inventor of checkers wanted 1,000 gold coins per day. The inventor of chess wanted one grain of rice on the first day, but the amount doubled every following day. How much rice would that be on the last day?



I very much like your focus on "why" and your many beautiful examples.

They bring to mind a few more reasons for "why" we have math:

  • As the basis for a caste system based on how much math you have passed. A way of controlling who is in what profession, for example.
  • As a way of treating people differently (through rates, credit scores, incomes, etc.) without them having full knowledge or even understanding what its all about.
  • As a way of making our systems just incomprehensible enough to most people so that they can't argue with them. For example, most people think that banks loan out money based on the deposits they have. But actually, the central banking system and participating banks are chartered by the government to create loans in an amount ten times or more than whatever assets a bank has; but nobody creates the money needed to pay the interest on those loans, which grows exponentially; which might be all right if the economy itself grew exponentially; but we have thereby legislated the need to grow exponentially, naturally or (when that fails) otherwise; thus the pressure to (artificially) monetize everything in sight; and to prey on the most vulnerable (a major reason why ghettos persist, I think). So that bubbles (based on money for money's sake) are inevitable. Similarly, the recent housing crisis was an application of math.
  • Math also lets us model realities in ways that let us suspend thinking about the underlying meaning. Which is essential for modern warfare.

Computers (and all systems) likewise allow us to ignore the underlying meaning. Social software is in a large part a way to avoid human contact by controlling it in very rigid channels.

Joe, my examples are negative, but I think the positive side would be math for citizenship.

I suppose that a distinction can be made between what must be taught-learned and what should be optional. I once thought that what really need to be taught is ethics, what is right and wrong. For example, language should be taught as a way of empathizing with others and ourselves, of caring about them. Math should be taught as the study of systems, especially the systems that we find ourselves in. It's morally essential for citizens in our modern world to distinguish between linear, exponential and periodic behavior and appreciate the implications. Overall, I imagine having a required school of just maybe two hours a day but that focused only on what is agreed to be absolutely essential. Which I think would include drill of "math facts" (multiplication tables, etc.) And most adults as well would be required to regularly show competence. Then the rest of education would all be optional.

About myself: I participated on this list about five years ago. I'm in Lithuania now. I will reintroduce myself but I was moved by Joe's letter and I could not keep from writing my own thoughts. I'm glad to see this list so lively with participants from before and I think new ones as well.



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Puslapis paskutinį kartą pakeistas 2016 rugsėjo 01 d., 23:25